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On the crack growth resistance of shape memory alloys

With the increasing use of shape memory alloys in recent years, it is important to investigate the effect of cracks. Theoretically, the stress field near the crack tip is unbounded. Hence, a stress-induced transformation occurs, and the martensite phase is expected to appear in the neighborhood of the crack tip, from the very first loading step. In that case, the crack tip region is not governed by the far field stress, but rather by the crack tip stress field. This behavior implies transformation toughening or softening.

The main objective of this study is to obtain the transformation toughening behavior of shape memory alloys. The energy dissipation caused by the high stresses in the transformation zone in the vicinity of the crack tip plays a major role in the transformation toughening of the alloy. Since this  issipation depends upon crack advance, the outcome of this approach is a crack growth resistance curve.

In this study, the transformation toughening behavior of a slowly propagating crack in a shape memory alloy under plane strain conditions and mode I deformation is numerically investigated. A  mall scale transformation zone is assumed.  A cohesive zone model is implemented to simulate crack growth within a finite element scheme. Resistance curves are obtained for a range of parameters that specify the cohesive traction-separation constitutive law. It is found that the choice of the cohesive strength t0 has a great influence on the toughening behavior of the material. Moreover,  the reversibility of the transformation can significantly reduce the toughening of the alloy. The shape of the initial transformation zone, as well as that of a growing crack is determined.  The effect of the Young's moduli ratio of the martensite and austenite phases is examined.

Recently, Yuval Freed and Leslie Banks-Sills wrote a paper entitled: "Crack growth resistance of shape memory alloys by means of a cohesive zone model". This paper was accpeted for publication at the Journal of the Mechanics and Physics of Solids. 

 A post-print file is attached here.

PDF icon sma-rev3.pdf1.26 MB


alinojumi's picture

Hi Dear Yuval

I am Ali Nojoumi a M.Sc. Civil engineer and I'm modeing shape memory alloys

using in concrete shear walls to reduce the effects of earthquakes...

making my Model by ABAQUS, I should use UserSubroutine to define such

SuperElastic behavior How can I manage that and if you have ever done this?

I would be glad to have your suggestions.

thank alot; AliNojumi@GMAIL

but I believe that it is not that difficult.

In general, you need to:

1. Obtain the stresses, inelastic strains and internal variables using a radial return mapping.

2. Obtain the consistent tangent modulus matrix.

Since I'm not familier with ABAQUS, I can't tell you how to do it specifically. Have a look at the 'help file' of ABAQUS.

Good luck.   


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